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Fuzzy bi-ideals in ordered semigroups

N KEHAYOPULU, M TSINGELIS
2005 Information Sciences  
The results on ordered semigroups can be transferred to fuzzy ordered semigroups, and from the results on fuzzy ordered semigroups one can get the corresponding results on ordered semigroups in the way  ...  So not only ordered semigroups give information about fuzzy ordered semigroups, but fuzzy ordered semigroups give information about ordered semigroups as well. 641 642 NIOVI KEHAYOPULU element a of S,  ...  In left simple ordered semigroups, the fuzzy bi-ideals are fuzzy right ideals. As a consequence, in left simple ordered semigroups, the bi-ideals are right ideals.  ... 
doi:10.1016/j.ins.2004.03.015 fatcat:7okeahlxyvdfhaayfkjyqs3lei

Generalized anti fuzzy bi-ideals in ordered semigroups

Young Bae Jun, Asghar Khan, Muhammad Shabir, Seok Zun Song
2010 Lobachevskii Journal of Mathematics  
Characterizations of an (∈, ∈ ∨ q k )-fuzzy bi-ideal in a semigroup S are discussed.  ...  The notion of (∈, ∈ ∨ q k )-fuzzy bi-ideals in a semigroup S is introduced, and several properties are investigated.  ...  As a generalization of fuzzy bi-ideals of a semigroup, Kazanci and Yamak [11] considered the generalized fuzzy bi-ideals of a semigroup.  ... 
doi:10.1134/s1995080210010105 fatcat:3hon7guvv5fuvipg6bops5xq3m

A NEW FORM OF FUZZY GENERALIZED BI-IDEALS IN ORDERED SEMIGROUPS

Hidayat Ullah Khan, Nor Haniza Sarmin, Asghar Khan
2014 Honam Mathematical Journal  
In this paper, we introduce the notion of (∈, ∈ ∨q k )-fuzzy subsystems of ordered semigroups namely (∈, ∈ ∨q k )-fuzzy generalized bi-ideals of ordered semigroups.  ...  The important milestone of the present paper is to link ordinary generalized bi-ideals and (∈, ∈ ∨q k )-fuzzy generalized bi-ideals.  ...  ordered semigroups in terms of (∈, ∈ ∨ q k )-fuzzy generalized bi-ideals and (∈, ∈ ∨ q k )-fuzzy left (right)-ideals.  ... 
doi:10.5831/hmj.2014.36.3.569 fatcat:i2cgmqs4gvfs3f77iujo27sh6u

A Novel Approach toward Fuzzy Generalized Bi-Ideals in Ordered Semigroups

Faiz Muhammad Khan, Nor Haniza Sarmin, Hidayat Ullah Khan
2014 The Scientific World Journal  
In this paper, we introduced a new and advanced generalization of fuzzy generalized bi-ideals of ordered semigroups. These new concepts are supported by suitable examples.  ...  These new notions are the generalizations of ordinary fuzzy generalized bi-ideals of ordered semigroups.  ...  semigroups in terms of ( , )-fuzzy generalized bi-ideals.  ... 
doi:10.1155/2014/275947 pmid:24883375 pmcid:PMC4030498 fatcat:gl2tge7p2jfk3dzsv6cuonxpha

Fuzzy Generalized Bi–Γ–Ideals of Type (λ, θ) In Ordered Γ–Semigroups

Faiz Muhammad Khan, Nor Haniza Sarmin, Asghar Khan
2013 Jurnal Teknologi  
Iampan [10] proposed the concept of (0-)minimal and maximal ordered bi-ideals in ordered Г-semigroups, and give some characterizations of (0-)minimal and maximal ordered bi-ideals in ordered Г-semigroups  ...  [16] characterized ordered Г-semigroups in terms of fuzzy interior Г-ideals and discussed some interesting properties of fuzzy interior Г-ideals in ordered Г-semigroups.  ... 
doi:10.11113/jt.v62.1881 fatcat:fqke6fehvjavfh42mgv4gqvkz4

Some New Characterization of Ordered Semigroups in Terms of \((\lambda ,\theta )\)-Fuzzy bi-ideals

Faiz Muhammad Khan, Nor Haniza Sarmin, Asghar Khan
2012 International Journal of Algebra and Statistics  
In this paper, we demonstrate a new concept of fuzzy bi-ideals called a (λ, θ)-fuzzy bi-ideals of an ordered semigroup.  ...  Finally, the characterization of completely ordered semigroups in terms of (λ, θ)-fuzzy bi-ideals is given.  ...  (see [9] ) gave the concept of a generalized fuzzy bi-ideal in ordered semigroups and characterized regular ordered semigroups in terms of this notion. Davvaz et al.  ... 
doi:10.20454/ijas.2012.376 fatcat:amd6jhhpknbmjmnvigbfjliple

New fuzzy generalized bi Γ-ideals of the type (∈,∈∨qk) in ordered Γ-semigroups

Ibrahim Gambo, Nor Haniza Sarmin, Hidayat Ullah Khan, Faiz Muhammad Khan
2017 Malaysian Journal of Fundamental and Applied Sciences  
In this paper, we provide an extension of fuzzy generalized bi Γ-ideals and introduce (∈,∈∨qk)-fuzzy generalized bi Γ-ideals of ordered Γ-semigroup.  ...  Ordered Γ-semigroup (generalization of ordered semigroups) play an important role in the broad study of ordered semigroups.  ...  of fuzzy generalized bi ideals in the structure of ordered semigroup.  ... 
doi:10.11113/mjfas.v13n4.756 fatcat:3hwqw3ruuvav5dnt3p7eft6oi4

COINCIDENCES OF DIFFERENT TYPES OF FUZZY IDEALS IN ORDERED Γ-SEMIGROUPS

Arunothai Kanlaya, Aiyared Iampan
2014 Korean Journal of Mathematics  
In 2008, Shabir and Khan [29] defined fuzzy bi-ideal subsets and fuzzy bi-filters in ordered semigroups and characterized ordered semigroups in terms of fuzzy bi-ideal subsets and fuzzy bi-filters.  ...  Abdullah, Aslam, Davvaz and Naeem [1] characterized the (∈, ∈ ∨q)-fuzzy bi-ideals in ordered semigroups. Coincidences of different types of fuzzy ideals in ordered Γ-semigroups 369  ...  Therefore, we will study the coincidences of fuzzy generalized bi-ideals, fuzzy bi-ideals, fuzzy interior ideals and fuzzy ideals in ordered Γ-semigroups.  ... 
doi:10.11568/kjm.2014.22.2.367 fatcat:iuh7dwpoezbi5c6siw3l5gjvpu

Characterizations of ordered semigroups by the properties of their fuzzy ideals

Muhammad Shabir, Asghar Khan
2010 Computers and Mathematics with Applications  
and right weakly regular ordered semigroups Ideals, quasi-ideals and bi-ideals Fuzzy ideals, fuzzy quasi-ideals and fuzzy bi-ideals a b s t r a c t In this paper we characterize different classes of ordered  ...  semigroups by the properties of their ideals, quasi-ideals and bi-ideals.  ...  The concept of a fuzzy generalized bi-ideal in ordered semigroups has been provided in [19] , where different classes of ordered semigroups have been characterized in terms of fuzzy generalized bi-ideals  ... 
doi:10.1016/j.camwa.2009.06.014 fatcat:vpbgf52gtvalfjavyz4mdomavm

Intuitionistic fuzzy semiprime ideals in ordered semigroups

Asghar Khan, Muhammad Shabir
2010 Russian Mathematics (Izvestiya VUZ. Matematika)  
We give further characterizations of regular and intra-regular ordered semigroups in terms of intuitionistic fuzzy left (respectively, right) ideals.  ...  In conclusion of this paper we prove that an ordered semigroup S is left weakly regular if and only if every intuitionistic fuzzy left ideal of S is idempotent.  ...  On the other hand, fuzzy generalized bi-ideals and fuzzy ideals in semigroups are adduced in [18, 19] .  ... 
doi:10.3103/s1066369x10050087 fatcat:mofzvp56lnhepkj3lfurc3bczq

The characterization of regular ordered Gamma semigroups in terms of (E,EVq_k)-fuzzy Gamma ideals

Ibrahim Gambo, Nor Haniza Sarmin, Hidayat Ullah Khan, Muhammad Faiz Khan
2017 Malaysian Journal of Fundamental and Applied Sciences  
In this paper, we give more generalized form of regular ordered gamma semigroups in terms of (E,EVq_k)-fuzzy gamma ideals.  ...  Some necessary and sufficient conditions for ordered gamma semigroup to be completely regular are provided in this paper.  ...  Kazancı and Yamak (2008) introduced the concept of a generalized fuzzy bi-ideal in semigroups where they studied   , q    fuzzy bi-ideal in a semigroup.  ... 
doi:10.11113/mjfas.v0n0.608 fatcat:ar7teyxmkjcfxe6xpoai6r6l7m

On fuzzy ordered semigroups

Muhammad Shabir, Asghar Khan
2014 Information Sciences  
We introduced the notions of upper (lower) rough ideal, bi-ideal, prime ideal and also the notions of upper (lower) rough fuzzy ideal, rough prime fuzzy ideal in ordered semigroups.  ...  In this paper we initiated the study of roughness in ordered semigroups based on pseudoorder.  ...  We introduced the notions of upper (lower) rough ideal, bi-ideal, prime ideal and also upper (lower) rough fuzzy ideal, rough fuzzy prime ideal in ordered semigroups.  ... 
doi:10.1016/j.ins.2014.02.107 fatcat:py7kfedfbbckdox3vggal5doye

Characterizations Of Ordered Semigroups By (∈,∈ ∨Q)-Fuzzy Ideals

Jian Tang
2012 Zenodo  
In this paper we first introduce the concepts of (∈,∈ ∨q)-fuzzy ideals, (∈,∈ ∨q)-fuzzy bi-ideals and (∈,∈ ∨q)-fuzzy generalized bi-ideals of an ordered semigroup S, and investigate their related properties  ...  Finally, characterizations of regular ordered semigroups and intra-regular ordered semigroups by means of the lower part of (∈ ,∈ ∨q)-fuzzy left ideals, (∈,∈ ∨q)-fuzzy right ideals and (∈,∈ ∨q)- fuzzy  ...  In [10] [11] [12] , Kuroki gave some properties of fuzzy ideals and fuzzy bi-ideals and fuzzy generalized bi-ideals of semigroups (without order) and characterized regular semigroups, intra-regular semigroups  ... 
doi:10.5281/zenodo.1080702 fatcat:itztemvywjfdbnhhnxa6tewu7q

Prime bi-Ideals of $\Gamma $-Semigroups

Muhammad Shabir
2012 Journal of Advanced Research in Pure Mathematics  
In this paper, we introduce and study the prime, strongly prime, semiprime and irreducible fuzzy bi-ideals of a semigroup. We characterize those semigroups for which each fuzzy bi-ideal is semiprime.  ...  We also characterize those semigroups for which each fuzzy bi-ideal is strongly prime.  ...  Semigroups in which each Fuzzy Bi-ideal is Strongly Prime In this section we study those semigroups in which each fuzzy bi-ideal is semiprime.  ... 
doi:10.5373/jarpm.788.021711 fatcat:5umexpa3d5bqxhkrj3m65j4k6m

(λ,μ)-Fuzzy Version of Ideals, Interior Ideals, Quasi-Ideals, and Bi-Ideals

Yuming Feng, P. Corsini
2012 Journal of Applied Mathematics  
We introduced(λ,μ)-fuzzy ideals,(λ,μ)-fuzzy interior ideals,(λ,μ)-fuzzy quasi-ideals, and(λ,μ)-fuzzy bi-ideals of an ordered semigroup and studied them.  ...  Whenλ=0andμ=1, we meet the ordinary fuzzy ones. This paper can be seen as a generalization of Kehayopulu and Tsingelis (2006), Kehayopulu and Tsingelis (2007), and Yao (2009).  ...  ; 3 in an ordered semigroup, every λ, μ -fuzzy quasi-ideal is a λ, μ -fuzzy bi-ideal; 4 in a regular ordered semigroup, the λ, μ -fuzzy quasi-ideals and the λ, μ -fuzzy bi-ideals coincide.  ... 
doi:10.1155/2012/425890 fatcat:let766n5dnbondey5ywrt76kwa
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